Questions

• Inequalities and Linear Programming Represent the graphs of linear inequalities in two unknowns in the rectangular coordinate plane Solve systems of linear inequalities in two unknowns

  如果$P(a, b)$是一個點，其中$a$和$b$滿足不等式系統$\left\{\begin{array}{c}a \geq b+1 \\ a \geq 0 \\ b \geq 0\end{array}\right.$，那麼在圖中$P$點可能位於哪個區域？

  2024

• Linear Equations in Two Unknowns plot and explore the graphs of linear equations in 2 unknowns formulate and solve simultaneous equations by algebraic and graphical methods

  如果 $ax-by-1=0$ 和 $cx-dy-1=0$，則 $x=$

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• Linear Inequalities in One Unknown explore the fundamental properties and some laws of inequalities solve simple linear inequalities in one unknown and represent the solution on the number line

  給定$x$是一個自然數，那麼$-\frac{3 x+2}{2}>5$和$x<2 x+11$的解為

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• Coordinate Geometry of Straight Lines

  $A, B$和$C$是直角坐標平面上的三個不同點。假設點$A$相對於$x$軸反射到點$B$，並順時針旋轉$90^{\circ}$到點$C$，那麼$B C$的方程是什麼？

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• Coordinate Geometry of Straight Lines understand and use formulas of distance and slope use ratio to find the coordinates of the internal point of division and mid-point

  在圖中，直線$L$的方程式為$ax+by-5=0$。如果由$L$和軸線所圍成的區域面積超過4，則以下哪些是正確的？ I. $a>0$ II. $b>2.5$ III. $2a>b$

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• Coordinate Geometry of Straight Lines understand and use formulas of distance and slope understand the conditions for parallel lines and perpendicular lines

  假設直線$L_{1}: ax+by+2=0$和$L_{2}: cx+5y-1=0$有無限多個交點。求$2a+3b+4c$的值。

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• Linear Equations in Two Unknowns plot and explore the graphs of linear equations in 2 unknowns formulate and solve simultaneous equations by algebraic and graphical methods

  

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• Coordinate Geometry of Straight Lines

  在圖中，$ABCD$是一個正方形，$\triangle CDE$是一個等邊三角形。$F$和$G$分別是$AD$和$BC$上的點。已知$AF=2\mathrm{~cm}，GC=3\mathrm{~cm}$且$AB=10\mathrm{~cm}。$FG$分別在$DE$和$CE$上交於$H$和$K$。求$HK$的長度。

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• Inequalities and Linear Programming Solve systems of linear inequalities in two unknowns Solve linear programming problems

  考慮以下線性不等式系統： $$ \left\{\begin{array}{c} x-2 y \leq 15 \\ 3 x-y \geq-5 \\ x+3 y \leq 15 \\ y \geq-2 x \end{array}\right. $$ 設 $R$ 為上述不等式系統解的區域，且 $(x, y)$ 為位於 $R$ 內的一點。若 $T=x^{2}+y^{2}-10 x-2 y+2020$，求 $T$ 的值域。

  2024

• Coordinate Geometry of Straight Lines

  設 $O$ 為原點。如果點 $A$ 的坐標是 $(0,8)$，且 $\triangle O A B$ 的外心的 $x$-坐標是 5，那麼以下哪個不能是 $B$ 的 $x$-坐標？

  2024